Calculate the mle estimate for mean, Applied Statistics

Assignment Help:

Each section of the SAT test is supposed to be distributed normally with a mean of 500 and a standard deviation of 100. Suppose 5 students in a class took the SAT math test. They received the following scores: 400, 450, 575, 600, and 625.

(a) Assuming a normal distribution, write out the likelihood function for estimating the mean μ and standard deviation σ of the average class score.

(b) Calculate the MLE estimate for μ and the standard deviation (σ) for this class.

(c) What is the value of the log-likelihood function at this estimate?

(d) What is the least-squares estimate for μ and σ in your data? Are there any differences? Why or why not?

(e) Using a likelihood-ratio test, test whether the MLE estimates from the class are significantly different from the national mean of 500 and national standard deviation of 100.

(Hint: Start by plugging those values into your log-likelihood function. Remember you are testing two restrictions).


Related Discussions:- Calculate the mle estimate for mean

Business reporting and analysis, You are a business analyst working for a c...

You are a business analyst working for a company called Combined Computers Pty Ltd. You have been asked to prepare a business report with statistics in it for the managing director

Linear regression mode, The State Department of Taxation wishes to investig...

The State Department of Taxation wishes to investigate the effect of experience, x, on the amount of time, y, required to fill out Form ST 1040AVG, the state income-averaging form.

Sensitivity and Specificity tests, The prevalence of undetected diabetes in...

The prevalence of undetected diabetes in a population to be screened is approximately 1.5% and it is assumed that 10,000 persons will be screened. The screening test will measure

Hi, i want assignmrnt help

i want assignmrnt help

Large sample test for proportion, Large Sample Test for Proportion A ra...

Large Sample Test for Proportion A random sample of size n (n > 30) has a sample proportion p of members possessing a certain attribute (success). To test the hypothesis that t

Agreement, Agreement The degree to which different observers, raters or ...

Agreement The degree to which different observers, raters or diagnostic the tests agree on the binary classification. Measures of agreement like that of the kappa coefficient qu

Level of significance, Level of Significance: α The main purpose of hyp...

Level of Significance: α The main purpose of hypothesis testing is not to question the computed value of the sample statistic, but to make judgment about the difference between

Coefficient of variation, Coefficient of Variation or C.V. To compare t...

Coefficient of Variation or C.V. To compare the variability between or more series, coeffiecnt of variation is used, it is relative measure of dispersion, it innovated and used

., Theories of Business forecasting

Theories of Business forecasting

Assumptions in anova, Assumptions in ANOVA The various populations f...

Assumptions in ANOVA The various populations from which the samples are drawn should be normal and have the same variance. The requirement of normality can be discarded if t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd